Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 577 · 40 questions

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

1. 1.In which quadrant does the point (3, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
2. 2.What is the midpoint of the line joining (9, 8) and (19, 10)? (a) (5, 1) (b) (9, 14) (c) (14, 9) (d) (28, 18)
3. 3.What is the distance between the points (9, 9) and (24, 17)? (a) 23 (b) 289 (c) 18 (d) 17
4. 4.In which quadrant does the point (4, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
5. 5.In which quadrant does the point (3, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
7. 7.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
9. 9.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
10. 10.What is the distance between the points (1, 12) and (17, 0)? (a) 21 (b) 400 (c) 20 (d) 28
11. 11.What is the distance between the points (1, 1) and (9, 7)? (a) 14 (b) 100 (c) 11 (d) 10
12. 12.In which quadrant does the point (5, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
13. 13.In which quadrant does the point (6, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
14. 14.In which quadrant does the point (−8, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
15. 15.What is the distance between the points (7, 16) and (16, 4)? (a) 16 (b) 21 (c) 225 (d) 15
16. 16.In which quadrant does the point (8, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
17. 17.What is the distance between the points (8, 8) and (15, 32)? (a) 31 (b) 26 (c) 25 (d) 625
18. 18.What is the distance between the points (8, 9) and (20, 0)? (a) 16 (b) 225 (c) 21 (d) 15
19. 19.What is the distance between the points (6, 9) and (18, 4)? (a) 13 (b) 169 (c) 17 (d) 14
20. 20.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
21. 21.What is the midpoint of the line joining (4, 2) and (6, 6)? (a) (5, 4) (b) (1, 2) (c) (4, 5) (d) (10, 8)
22. 22.What is the distance between the points (0, 6) and (9, 18)? (a) 21 (b) 15 (c) 225 (d) 16
23. 23.What is the distance between the points (7, 15) and (15, 9)? (a) 11 (b) 14 (c) 100 (d) 10
24. 24.In which quadrant does the point (−1, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
25. 25.What is the midpoint of the line joining (7, 13) and (15, 5)? (a) (22, 18) (b) (11, 9) (c) (9, 11) (d) (4, 4)
26. 26.What is the distance between the points (3, 17) and (19, 5)? (a) 21 (b) 20 (c) 28 (d) 400
27. 27.What is the distance between the points (1, 6) and (9, 0)? (a) 100 (b) 11 (c) 14 (d) 10
28. 28.What is the midpoint of the line joining (10, 9) and (22, 1)? (a) (32, 10) (b) (6, 4) (c) (16, 5) (d) (5, 16)
29. 29.In which quadrant does the point (−2, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
30. 30.In which quadrant does the point (−1, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
31. 31.What is the midpoint of the line joining (8, 8) and (10, 0)? (a) (9, 4) (b) (18, 8) (c) (4, 9) (d) (1, 4)
32. 32.In which quadrant does the point (−8, −8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
33. 33.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
34. 34.What is the midpoint of the line joining (0, 10) and (12, 22)? (a) (12, 32) (b) (6, 16) (c) (6, 6) (d) (16, 6)
35. 35.What is the midpoint of the line joining (1, 9) and (13, 3)? (a) (6, 7) (b) (7, 6) (c) (6, 3) (d) (14, 12)
36. 36.What is the distance between the points (4, 2) and (20, 14)? (a) 21 (b) 20 (c) 400 (d) 28
37. 37.What is the midpoint of the line joining (5, 9) and (7, 3)? (a) (6, 6) (b) (12, 12) (c) (7, 6) (d) (1, 3)
38. 38.What is the midpoint of the line joining (6, 8) and (16, 20)? (a) (5, 6) (b) (22, 28) (c) (14, 11) (d) (11, 14)
39. 39.What is the midpoint of the line joining (7, 1) and (17, 3)? (a) (2, 12) (b) (24, 4) (c) (12, 2) (d) (5, 1)
40. 40.What is the midpoint of the line joining (5, 6) and (9, 12)? (a) (14, 18) (b) (9, 7) (c) (2, 3) (d) (7, 9)

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad